This invention relates to data processing systems, methods and computer program products, and more particularly to statistical systems, methods and computer program products.
Sampling plans are widely used in manufacturing environments in order to determine whether items are being manufactured at a desired quality level. In order to construct a sampling plan, the ANSI/ASQ Z1.9 standard generally is used. The ANSI/ASQ Z1.9 standard is a collection of sampling plans presented in tabular and graphical form. In order to construct a sampling plan, the ANSI/ASQ Z1.9 standard is studied, and a sampling plan which best matches a desired sampling plan is selected.
Unfortunately, in using the ANSI/ASQ Z1.9 standard, the user may be bound to those sampling plans that are set forth in the standard. In particular, specific values of error rates, power, sample size and other parameters may be forced upon a user because the tables may not include the exact criteria that are desired by a given user.
Moreover, because the ANSI/ASQ Z1.9 standard uses test procedures that are based on a non-central t distribution, it may be difficult for the user to interpolate or extrapolate between tables of the standard. Notwithstanding these difficulties, the ANSI/ASQ Z1.9 standard continues to be widely used in constructing sampling plans for items that are manufactured.
It is therefore an object of the present invention to provide improved systems, methods and computer program products for constructing sampling plans for items that are manufactured.
It is another object of the present invention to provide systems, methods and computer program products for constructing sampling plans that can be flexible to meet the needs of a particular user and manufacturing process.
These and other objects are provided, according to the present invention, by inputting into a computer a desired Acceptable Quality Limit (AQL), a desired Key Defect Rate (KDR), a desired power of a sampling plan for the items that are manufactured and a desired false alarm rate for the sampling plan. The computer then calculates a required sample size to provide the desired AQL, the desired KDR, the desired power of the sampling plan for the items that are manufactured and the desired false alarm rate for the sampling plan. Thus, each of the individual parameters may be independently specified based on the items that are manufactured, desired AQLs, KDRs, power and false alarm rates. Reliance on ANSI/ASQ Z1.9 tables which might best fit a user""s desired parameters can be reduced and preferably eliminated.
In addition to calculating the required sample size, a decision rule critical value also may be calculated based upon the required sample size to provide the desired AQL, the desired KDR, the desired power and the desired false alarm rate for the sampling plan. Following the calculations, a relationship between sample size, acceptable number of defective items and false alarm rate automatically may be graphically displayed based upon the desired AQL, the desired KDR and the desired power of the sampling plan.
The items that are manufactured may then be sampled at the required sample size to obtain samples, and the number of defective items in the samples or other response variables in each of the samples, may be measured. After measuring the response variables, such as the number of defective items, the measured response variable for each of the samples is input into the computer and an estimate of the Quality Level (QL) for the items that are manufactured is calculated, based on the measured response variable for each of the samples.
Prior to calculating the required sample size and the decision rule critical value, a sample distribution that is variance invariant may be calculated based on a normal distribution. A percentile grid of sample size and a true process defect rate is formulated based on estimated percentiles of a cumulative distribution of the sampling distribution. A bias-corrected percentile grid of sample size and the true process defect rate is then formulated from the percentile grid. The bias-corrected percentile grid is stored in the computer.
The bias-corrected percentile grid may be used to compute the decision rule critical value from the AQL and the false alarm rate, across a plurality of sample sizes. The bias-corrected percentile grid is evaluated for the decision rule critical value, to determine the required sample size. More particularly, the decision rule critical value is computed from the AQL, the false alarm rate and the desired sample size using the bias-corrected percentile grid of sample size and a true process defect rate. The bias-corrected percentile grid is evaluated for values that are larger than the AQL, with the percentile being the desired power.
After the measured response variable for each of the samples is input into the computer, an estimate of the QL may be calculated by computing a bias correction coefficient. A QL test statistic is computed as a function of the bias correction coefficient and at least one quantile from a cumulative distribution function of a central t distribution, with at least one argument that is a function of a sample mean, a sample standard deviation, the sample size and a specification limit. The computer automatically can determine whether the QL test statistic is at least equal to the decision rule critical value.
In another aspect of the invention, after the measured response variables are input to the computer, the computer calculates a point estimate of the number of out-of-specification items that are manufactured based on the measured response variable for each of the samples.
In addition to calculating a required sample size as was described above, the present invention also may be used to calculate a KDR that is produced from a desired sample size. In particular, a desired sample size, a desired false alarm rate, a desired AQL and a desired power are input into a computer. The computer calculates a KDR that is produced from the desired sample size, the desired false alarm rate, the desired AQL and the desired power of the sampling plan for the items that are manufactured. Thus, given a desired sample rate, a KDR may be calculated.
The KDR may be calculated by computing a decision rule critical value based on the desired AQL and the desired false alarm rate for the desired sample size. After the KDR is calculated, a relationship between acceptable number of defective items and false alarm rate may be graphically displayed based on the desired AQL, the desired KDR and the desired power of the sampling plan.
As described above, after the calculation is made, the items may be sampled at the desired sample size to obtain samples, and a KDR of the items that are manufactured may be determined from the samples. After the items are sampled, the measured response variable for each of the samples may be provided to the computer, and the computer can calculate an estimate of the KDR, so that the estimate of the KDR can be compared to the KDR that was calculated. After providing the computer with the measured response variable for each of the samples, a point estimate of a process defect rate for the items that are manufactured also may be calculated based on the measured response variable for each of the samples.
The present invention may be embodied in one or more spreadsheets with an efficient user interface. The spreadsheets may be used in lieu of the ANSI/ASQ Z1.9 standard, to allow flexible sampling plans to be constructed and the results of sampling to be measured without the need to fit the desired sampling plan to conform to one of the series of charts in the ANSI/ASQ Z1.9 standard. It will be understood that the present invention may be embodied as systems, methods and/or computer program products.